The number 75 deserve to be written as the sum of the squares of 3 different positive integers. What is the amount of these 3 integers?

(A) 17(B) 16(C) 15(D) 14(E) 13

*This question is indigenous the totally free official GMAT exercise tests 1 and 2 so protect against if friend haven’t excellent those already.You are watching: The number 75 can be written*

## Define the question: What is the amount of this 3 integers?

Not much to define but I’d probably write out: X + Y + Z = ? to represent the sum.

## Setup

Most the this question is in the setup. Look for something come organize: The sum of the squares the the 3 different positive integers sum is 75. OK. So walk ahead and also list the first bunch of squares starting from 1 approximately just listed below 75. Once you’ve got that you simply need to find the mix that works.

1

4

9

16

25

36

49

64

81 (TOO BIG)

## Solve

Before you start writing prefer crazy come up v a mini-plan. Is over there anything in the concern to overview your work? In this case let’s look at the constraints:

**75** can be composed as the amount of the squares the 3 various positive integers

We need to sum come 75 for this reason let’s start from the larger integers (that will certainly take up much more of the space) and also work under to to fill in what’s left over. Why? To obtain to 75 you’re walking to require one the those big guys (64, 49, or 36).

Finding a constraint deserve to be very helpful. Usually with these GMAT puzzles over there are little shortcuts. Generally you don’t pull them the end of thin air. They are the natural conclusion of great organization. Make certain to take your time with setup so girlfriend pave the means for success. Here’s one more GMAT question that depends on simply staying organized and also paying attention: for a particular race, 3 groups were enabled to enter 3 members each. A team deserve 6 – n clues whenever one of its members perfect in nth place, wherein 1 ≤ n ≤ 5. The details are really different however the style is comparable and i think it needs the very same kind the thinking.

**OK, earlier to solving!**

Starting through 64.

64 + ? = 75

We require 11 to with 75. So look at your list and also see if the amount of any type of of the two integers equates to 11. Not possible. 64 is out.

Let’s carry out the very same thing v 49.

49 + ? = 75

We require 26. Scan the list. Bingo: 25 + 1. Easy.

We need the amount of the squares the those for this reason 7 + 5 + 1 = 13.

What is the sum of these 3 integers? 13. E.

## Takeaways

-Do simple organization. Make list, do a diagram, do a chart… execute something with details given. From basic setup come more complicated inferences.

-Focus on limit or every little thing parameters you have the right to in the concern to overview your follow through. Always shot to come up with a mini-execution plan!

## Video Solution: The number 75 can be composed as the amount of the squares the 3 various positive integers. What is the sum of these 3 integers?

## Additional GMAT Number Properties, Puzzle, Constraints practice Questions

As mentioned over this questions has actually a very similar vibe in terms of the an easy organizing and also using constraints to solve: for a certain race, 3 groups were permitted to get in 3 members each. A team earn 6 – n point out whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.

See more: What Is The Climax Of The Giver Plot Diagram Storyboard, What Is The Climax Of The Giver By Lois Lowry

Here’s an additional GMAT puzzle that is a bit different however can likewise be resolved with a comparable style of simple organizing: If x and y are positive integers such that y is a lot of of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

Here’s a challenging question indigenous the GMAT prepare tests 1 and 2 that calls for a similar collection of tools: If each term in the sum a1 + a2 + a3 +…+ one is one of two people 7 or 77 and also the sum equals 350, i m sorry of the following can be same to n?

And here’s a puzzle from GMAT concern of the work that also benefits from just obtaining the info from the concern in shape.